A fundamental problem faced by the brain is posed by the fact that the activity of individual neurons is noisy - an identical stimulus presented many times will elicit different response rates. This stimulus-independent spike-rate variability tends to be weakly correlated between neuronal pairs in sensory cortex. It is frequently suggested that these noise correlations reflect the stochastic nature of the afferent pathways that encode sensory input. Importantly, these correlations can place hard limits on the fidelity of sensory encoding. When combining the outputs of many neurons, noise that is independent across neurons makes negligible contribution. However, noise that is shared by neurons remains in the combined output. The extent to which correlated noise limits the brains ability to represent information about the external world depends on the exact structure of the correlations. A long history of theoretical work has identified the conditions under which correlations are information-limiting. However, this work all assumes that the source of these correlations is in the sensory afferents, which means they are not known to the rest of the brain. If some part of the noise correlation in sensory populations is generated by centrally generated signals, then a decoder with access to these signals could achieve much higher performance that current theoretical work suggests. We tested directly, for the first time, whether the structure of noise correlations in visual cortex reflects signals of central origin during perceptual decision making. Our approach was to measure noise correlations in contexts where task instruction changed but the retinal input remained constant. We recorded single-unit spiking activity in small populations of primary visual cortical (V1) neurons in awake rhesus monkeys, while they performed a coarse orientation discrimination with orientation-filtered noise. Subjects had to discriminate two orthogonal orientations, which were fixed in a given recording session but which were varied between sessions. We found that the structure of noise correlations changed dynamically with the instructed task, even on zero-signal trials which were statistically identical in all tasks. Specifically, pairs of neurons which represented the same choice orientation were more highly correlated than pairs representing opposite choices. Pairs not well tuned for the task showed no modulation. These task-dependent changes in correlation structure closely matched the structure of information-limiting correlations. At first sight, these dynamic changes appear not to have a beneficial impact on the information capacity of visual cortex. However, if downstream areas distinguish inputs of central and peripheral origin, then the observed structure of correlations in the sensory population no longer determines an information-limit. This radically changes our understanding of how sensory stimuli can be encoded in populations of neurons.